The Catalan giants have managed to ease their financial problems, but the club are still in a difficult situation and need to trim their squad this summer in order to bring in new signings.
Mingueza made 27 appearances for Barcelona last season, including 19 outings in La Liga, showing his versatility by operating as a right-back and centre-back in 2021-22.
The 23-year-old only has 12 months left to run on his contract at Camp Nou, though, and has allegedly been told to find a new club ahead of the new season.
Puig, meanwhile, played 17 times for the Catalan giants last term, including featuring in their final four La Liga matches of the campaign against Real Betis, Celta Vigo, Getafe and Villarreal.
The Spaniard is down the pecking order when it comes to the midfield spots, though, with Kessie also set to move above him once the Ivory Coast international's switch is confirmed.
Umtiti only played once for Barcelona this season - against Osasuna in La Liga in December - and the Frenchman is finally expected to leave this summer following a host of speculation.
Braithwaite has also reportedly been told to leave, with the Denmark international struggling for football in the second half of last season after returning from a serious knee injury.
The 31-year-old started last season in impressive fashion, scoring twice and registering one assist in the team's first match against Real Sociedad, but he was out between September and January through injury and only played once in the second half of the campaign.
"I've played more in these four games than in the whole season there [at Barcelona]," Braithwaite told TV 2 SPORT earlier this month after featuring for his country. "It's been fantastic and I'm very happy with the confidence Kasper [Hjulmand] has given me."
The attacker has made 56 appearances for the La Liga giants in all competitions since his arrival from Leganes in February 2020, contributing 10 goals and five assists in the process.